Interactive step-by-step animation using GeoGebra. Post your solution in the comment box below.

Level: Mathematics Education, High School, Honors Geometry, College.

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## Wednesday, March 18, 2020

### Dynamic Geometry Problem1463: Parallelogram, Interior Point, Opposite Triangles with Equal Sum of Areas

Labels:
area,
GeoGebra,
internal,
ipad,
ipadpro,
parallelogram,
quadrilateral,
sum,
triangle

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Draw XPY parallel to BC & AD

ReplyDeleteIf S(BPX) = x & S(CPY) = y then S(APX) = S1-x & S(DPY) = S3-y

Easily x+y = S2 ….(1) and (S1-x) + (S3-y) = S4 …(2)

Adding (1) + (2) gives the desired result

Sumith Peiris

Moratuwa

Sri Lanka

Solution 2

ReplyDeleteLet AB = CD = a & BC = AD = b. Draw altitudes h1,h2,h3,h4 for the 4 Tr.s from P to the base

S1 + S3 = a(h1+h3)/2 = S(ABCD)/2 and S2 + S4 = b(h2+h4) = S(ABCD)/2 and the result follows.

Sumith Peiris

Moratuwa

Sri Lanka